Various mechanisms have been used for honing the bores of elliptical and other non round cylinders used in a few internal combustion engines and potentially usable in other devices. Some of these mechanisms apply constant hydraulic pressure in the process of metal removal. This method has a tendency to follow the original bore geometry rather than correcting it to a desired configuration. Some methods employ three dimensional grinding which generally requires excessive cycle time for commercial production use. U.S. Pat. No. 5,681,210, assigned to the assignee of the present invention, describes a mechanism including a barrel cam external to a conventional honing machine as the principal actuator for the contouring and expansion of honing stones.